A384146 - OEIS

A384146

Smallest squarefree order m > 0 for which there are n nonisomorphic finite groups of order m, or 0 if no such order exists.

1, 6, 609, 30, 273, 42, 903, 510, 8729, 3255, 494711, 210, 16951, 5115, 54431, 1218

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OFFSET

1,2

COMMENTS

It has been established that every n < 10000000 arises as the number of groups up to isomorphism of some squarefree m. That is, a(n) > 0 for n < 10000000.

It is conjectured that 0 never appears in this sequence.

LINKS

Table of n, a(n) for n=1..16.

J. H. Conway, Heiko Dietrich and E. A. O'Brien, Counting groups: gnus, moas and other exotica, Math. Intell., Vol. 30, No. 2, Spring 2008.

EXAMPLE

a(3)=609 since there are 3 groups of order 609 up to isomorphism, and 609 is the smallest squarefree integer such that there are 3 groups of that order.

CROSSREFS

Cf. A046057 (m not necessarily squarefree).

Sequence in context: A255886 A300389 A172899 * A222831 A206458 A265116

Adjacent sequences: A384143 A384144 A384145 * A384147 A384148 A384149

KEYWORD

nonn,more

AUTHOR

Robin Jones, May 21 2025

STATUS

approved